Algebra · Algebraic proof
Chapter 1 · 3
The idea
Proving divisibility results
The expand–collect–factorise engine: to prove "always a multiple of k", exhibit the expression as k × (whole number) — and say so.
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Algebra · Algebraic proof
Proving divisibility results
The expand–collect–factorise engine: to prove "always a multiple of k", exhibit the expression as k × (whole number) — and say so.
Why it works
The shape is k × (whole number)
"A multiple of " MEANS " times a whole number". So a divisibility proof has one goal: wrestle the expression into the exact shapeand then say that's what it is. The engine is always the same: encode → expand → collect → factorise out → conclude.
Watch it run — *the sum of five consecutive integers is a multiple of 5*:
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The rest of the explanation, plus 2 worked examples you step through move by move.
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